From the location that is just what I was thinking too - a tooth abscess.
A cracked tooth, or tartar build up, or periodontal disease can cause an infection in the nerve pulp of the tooth. Sometimes these abscess around the gumline and sometimes they go out the long root of an upper tooth into the face area. Its usually the carnassial tooth, the dog's fourth pre-molar tooth that this happens with. It's usually the biggest toothwith the longest of roots a dog has.
If the infection is going up to the face area you might not smell it in the mouth.
Dogs often don't chew their food. They are designed to gulp their food and let their intestinal tract break it down with acids and enzymes that are stronger than those found in a human stomach. Their teeth are designed more to cut meat in to chunks that can be swallowed so when fed dog food no chewing need be done so a dog can eat fine with a sore tooth.
This site goes over canine dentistry and even has a picture of a tooth abscess under the eye area as you scroll down
http://www.thepetcenter.com/gen/dental.html
Usually removing the tooth resolves the problem along with some antibiotics. I'd suggest a dental exam and cleaning and then removal of the diseased tooth if that is the problem as a good way to resolve this.
Hope this helps you!